Thyristor bridge rectifier (Fully controlled)

Question 1

What is the circuit for a fully controlled thyristor bridge rectifier with an inductive load?

Answer 1

[Picture15]

Question 2

Draw the graphs for v_S, v_O, i_O, i_S for a fully controlled thyristor bridge rectifier with an inductive load

Answer 2

[Picture16]

Question 3

What is the purpose of adding a highly inductive load?

Answer 3

> An inductor is normally used to improve the output current waveform

> If the inductor the inductor is sufficiently large (≈ ∞)then the output current constant.

Question 4

What is control parameter ‘a’

Answer 4

> For the control of T₁ and T₄ ‘a’ represents the angle difference between the 0 phase for v_S and the point when the pulse is applied to the gate of the thyristors.

> For the control of T₂ and T₃ ‘a’ represents the angle difference between the π phase for v_S and the point when the pulse is applied to the gate of the thyristors.

Question 5

For a 50Hz AC supply, where a = 36° when are T₁, T₂, T₃, T₄ applied?

Answer 5

T₁ & T₄ are applied 2ms after 0°

T₂ & T₃ are applied 2ms after π°

Question 6

Describe the operation of a fully controlled thyristor bridge rectifier for one full cycle

Answer 6

ωt = 0

> T₂ and T₃ turn off

ωt = a

> T₁ and T₄ are fired

> T₂ and T₃ remain off

ωt = a ⇒ ωt = a + π

> v_S = v_O

> i_S = i_O

ωt = π

> T₁ and T₄ turn off

ωt = π + a

> T₂ and T₃ are fired

> T₁ and T₄ remain off

ωt = π + a ⇒ ωt = a + 2π

> -v_S = v_O

> i_S = -i_O

ωt = 2π

> T₂ and T₃ turn off

Question 7

Draw the graphs for V_S, V_O for a fully controlled thyristor bridge rectifier with an inductive load for a = 0°, 30°, 60°

Answer 7

[Picture17]

Question 8

How is the average output voltage calculated?

Answer 8

V_Oavg = 1 / π ∫_a^a+π v_S dωt

Question 9

What is the simple equation for the output voltage in terms of the RMS value for the supply voltage and the value ‘a’? Derive it

Answer 9

V_Oavg = 0.9V_Scos⁡(a)

[Picture18]

Question 10

What is the equation to calculate the supply current harmonics? Where does it come from?

Answer 10

i_sh(t) = 4I_O / hπ × sin⁡[h(ωt - α)]

From Fourier analysis: i_s(t) = ∑_h=1^∞ i_sh(t)

Question 11

When does the equation for harmonics apply?

Answer 11

Only for odd values of h / odd harmonics

Question 12

What happens if we try and find the current supply for an even harmonic?

Answer 12

i_sh(t) = 0

Question 13

What is the equation to calculate the fundamental harmonic of a fully controlled thyristor bridge rectifier?

Answer 13

I_s1 ≈ 0.9I_O

Question 14

What is the equation for the first harmonic of current and the RMS input current for a fully controlled bridge rectifier?

Answer 14

I_s1 / I_s = 0.9

Question 15

What is the relationship for RMS input current and RMS output current?

Answer 15

I_S = I_O

Question 16

What are 2 equations for power on the AC side of a fully controlled thyristor bridge rectifier?

Answer 16

P = V_S × I_S1 × cos⁡(a)

P = 0.9 × V_S × I_O × cos⁡(a)

Question 17

What are 2 equations for the power factor on the AC side of a fully controlled thyristor bridge rectifier?

Answer 17

PF = (I_s1 / I_S) × DPF

PF = 0.9cos(α)

Question 18

What is the equation for the displacement power factor?

Answer 18

DPF = cos(α)

Question 19

What is the equation for the output power of a fully controlled thyristor bridge rectifier?

Answer 19

P_out = V_Oavg × I_O

Question 20

What is the equation for the input power of a fully controlled thyristor bridge rectifier?

Answer 20

P_in = V_S × I_S1 ×cos⁡(θ)

or

P_in = V_S × I_S1 × DPF

Question 21

What is the relationship of power for an ideal rectifier?

Answer 21

P_in = P_out

Question 22

What is the equation for power factor for and ideal rectifier in terms of RMS supply currents and voltages?

Answer 22

PF = P_out / (V_S × I_S)

Question 23

What is the equation for power factor for and ideal rectifier in terms of control parameter ‘a’?

Answer 23

PF = 0.9cos(α)